cInstitute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567;dDepartment of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095-1565

Significance

Submarine hot springs known as hydrothermal vents host unique ecosystems of endemic animals that do not depend on photosynthesis. Quantifying larval dispersal processes is essential to understanding gene flows and diversity distributions of vent endemic species, as well as to protect vent communities from anthropological disturbances (e.g., deep-sea mining). In this study, we assess the potential frequency of larval exchange between vent fields throughout the entire western Pacific via ocean circulation processes, so that population geneticists can make quantitative comparisons. We show that western Pacific vents in distant basins are potentially connected with strong directionality. This article makes a valuable contribution to a difficult and important area of deep ocean processes.

Abstract

Hydrothermal vent fields in the western Pacific Ocean are mostly distributed along spreading centers in submarine basins behind convergent plate boundaries. Larval dispersal resulting from deep-ocean circulations is one of the major factors influencing gene flow, diversity, and distributions of vent animals. By combining a biophysical model and deep-profiling float experiments, we quantify potential larval dispersal of vent species via ocean circulation in the western Pacific Ocean. We demonstrate that vent fields within back-arc basins could be well connected without particular directionality, whereas basin-to-basin dispersal is expected to occur infrequently, once in tens to hundreds of thousands of years, with clear dispersal barriers and directionality associated with ocean currents. The southwest Pacific vent complex, spanning more than 4,000 km, may be connected by the South Equatorial Current for species with a longer-than-average larval development time. Depending on larval dispersal depth, a strong western boundary current, the Kuroshio Current, could bridge vent fields from the Okinawa Trough to the Izu-Bonin Arc, which are 1,200 km apart. Outcomes of this study should help marine ecologists estimate gene flow among vent populations and design optimal marine conservation plans to protect one of the most unusual ecosystems on Earth.

Hydrothermal vent fields in the western Pacific have received substantially less attention than have eastern Pacific vents. Western Pacific vents are mostly distributed along spreading centers in submarine basins behind convergent plate boundaries, whereas those of the eastern Pacific occur mainly at midocean ridges. It is estimated that vent-endemic species in back-arc basins were introduced along now-extinct midocean ridges that bridged the eastern and western Pacific Oceans ∼55 million years ago, with a potential origin at the East Pacific Rise (1, 2). More recent studies suggest the possibility that Indian Ocean ridge systems once connected Atlantic and Pacific vent fields (3). Spreading centers in back-arc basins are active for typically 5–10 million years (4, 5). Thus, life spans of back-arc spreading centers are significantly longer than population lifetimes of vent animals observed in the eastern Pacific (∼1 million years) (6).

Recent genetic studies have addressed the matter of genetic differentiation among vent populations (7⇓⇓⇓–11). Genetic data imply that back-arc basin populations are well-mixed genetic pools (12, 13). In contrast, vent populations in distant basins (∼3,000 km apart) are genetically distinct, suggesting that occasional migrations may have occurred over the course of several hundred thousand generations (14). There is one example of a widespread species (Bathymodiolus septemdierum complex) occurring in all western Pacific back-arc basins (15). To interpret gene flows of vent species, it is necessary to understand larval dispersal by ocean circulation, as well as tectonic history (16⇓–18). However, quantitative data regarding dispersal processes in the western Pacific are still woefully inadequate, leaving many unanswered questions. Dispersal patterns among vent populations in the western Pacific basins have not been previously addressed.

Detailed observations and models for eastern Pacific vents have revealed mechanisms of near-bottom circulation strongly influenced by distinct topographic features of midocean ridges (19⇓⇓⇓–23). Conduit-like structures of midocean ridges may shield larvae from cross-axial dispersal and also may enable long-distance dispersal that connects distant vent fields (20). Similar long-dispersal mechanisms, however, do not apply to species in the western Pacific, where midocean ridges do not exist. If dispersal were limited to near-bottom depths, vent species of the western Pacific would largely be contained within a given back-arc basin.

Although most species likely remain near the bottom, some strong-swimming larvae (e.g., shrimp and crabs) may disperse higher in the water column, possibly ∼1,000 m above the bottom, where they can be transported by faster currents (24, 25). Lagrangian measurement methods, using deep-ocean profiling floats programmed to drift at a specified depth or constant density surface, can be used to measure dispersal in the water column. This approach has been used for hydrothermal vent surveys as well (26, 27). One example was the Lau Basin Float Experiment (27), which captured boundary currents within the back-arc basin and westward outflow from the basin resulting from the South Equatorial Current. For various reasons, it is challenging to quantify vent-to-vent transport using only in situ experiments; therefore, one promising approach is to combine dispersal experiments with ocean circulation models.

Properly analyzed, such observation and modeling data should yield reasonable estimates of dispersal processes by ocean circulation and should help marine ecologists understand biogeography and gene flow among vent populations in the western Pacific Ocean. We assessed potential larval dispersal from hydrothermal vent fields in the western Pacific on varying spatial scales, from intra- to interbasin vent communications, by integrating information from a deep-ocean profiling float experiment and predictions derived from an ocean circulation model.

Results and Discussion

Dispersal in a Back-Arc Basin.

As a base case, we focused on dispersal processes from a vent field in the Okinawa Trough. The Okinawa Trough is an active back-arc spreading basin behind the Ryukyu arc-trench system, where the Philippine Sea Plate subducts beneath the Eurasian Plate (Fig. 1). The current rifting started about 2 million years ago (28). Depths of vent fields in the Okinawa Trough registered in the InterRidge vents database (29) vary between 560 and 1,850 m, with a mean depth of 1,100 m.

Dispersal processes in the deep sea show complex eddy motions, changing monthly or more often. (A) Trajectories of deep-sea profiling floats released from Hatoma Knoll (indicated with white arrows) in the Okinawa Trough, illustrating dispersal originating at a vent field within a back-arc basin. Floats were deployed semimonthly in 2013 and 2014 on dates indicated at the bottom right corner of the figure. Float tracks until March 2015 are shown here. These passively transported floats maintain their depth 1,000 m below the sea surface and return to the surface every 30 d (circles). Positions of each float at the sea surface are connected with cubic splines. The numbers show the cumulative sum of surfacing events, which indicate approximate drift times in months. (B) Close-up view of the same trajectories for the first three surfacing events.

To assess spatial and temporal scales of dispersal at Hatoma Knoll (1,520 m) in the southern Okinawa Trough, we deployed 10 deep-ocean profiling floats (OPTIMARE NEMO-Floats), introduced semimonthly from spring to fall over the course of 2 y (April 17, 2013–October 25, 2014). These floats were preprogrammed to maintain a depth of 1,000 m while being passively transported by ocean currents. Floats continuously recorded data, and they surfaced every 30 d to transmit their coordinates (and a vertical water profile) to the Iridium satellite. One unit failed to surface; another stopped surfacing after 2 mo. All other floats continue to function. The descending and ascending speeds of floats are adjusted to minimize drift caused by the surfacing process. Long-distance movements of the floats are mostly a result of deep ocean circulation, and float trajectories allow us to understand dispersal from a single vent field (Drift at the Sea Surface).

Deployed floats traced complicated spaghetti-like patterns through the ocean, even 1,000 m below the sea surface, and surprisingly, even within semiclosed back-arc basins (Fig. 1A). Even at this dispersal depth, float trajectories are characterized by complicated time-dependent, chaotic, eddy-like motions having radii on the scale of 10s of kilometers, similar to those of shallow-water floats (30). Most floats remained in the southern part of the Okinawa Trough, although one float traveled more than 500 km to the northern Okinawa Trough. Long-distance larval dispersal probably occurs intermittently.

Temporal variability of flow is often measured with correlation timescales, representing characteristic periods during which flow remains more or less consistent in speed and direction. Correlation timescales could be qualitatively inferred from float tracks during the first several months of this study (Fig. 1B). Float deployments separated by ∼30 d or longer demonstrate different dispersal patterns, although some consecutive releases are similar. In other words, the Eulerian correlation time is less than 1 mo. We calculated the Eulerian correlation time (e-folding time) from time series of model flow fields. The estimated correlation time is about 2 wk, which is longer than that of the ocean surface (several days) (31), reflecting less energetic circulation. Current observation data from northern East Pacific Rise (32) appear to have a similar Eulerian correlation time.

Dispersal Probability.

Because of the unpredictable nature of dispersal, a large number of cases (degrees of freedom) are necessary to have sufficient statistical power. In the model domain, nearly 1 million simulated “model floats” were released from Hatoma Knoll. Similar to actual floats, model floats were passively transported by the simulated current at a constant depth of 1,000 m. By spatially binning the model float distribution for a given advection time, it is possible to evaluate a probability density function of float displacement (Lagrangian PDF), both descriptively and quantitatively (33). Comparisons of Lagrangian PDFs with movements of actual floats show reasonable qualitative agreement (Fig. 2A). The ocean circulation model quantifies dispersal from Hatoma Knoll well, assuming a dispersal depth of 1,000 m.

The ocean circulation model effectively quantifies potential larval dispersal from Hatoma Knoll. (A) Distributions of deep-profiling floats (cross markers) from Hatoma Knoll (white arrow) after 90 d of drifting 1,000 m below the sea surface show good agreement with predictions by the ocean circulation model (color contour). Colors indicate probability densities of float displacement per unit area (square kilometers). (B) Transport from Hatoma Knoll to other vent fields at a dispersal depth of 1,000 m (lines and numbers) deduced from the model. Five representative vent fields are shown. Numbers in brackets indicate the depth of each vent field. Drift time was set to the population mean for the mean temperature at a depth of 1,000 m (83 d). Numbers indicate the number of expected connections out of 100 million independent events. The number beside Hatoma Knoll represents likelihood of self-recruitment.

To quantify larval dispersal, among other things, we need a reasonable assessment of planktonic larval duration (PLD). Larval development of marine animals should be more protracted in deeper, colder water because of reduced metabolic rate. Water temperature declines rapidly with depth, but is rather consistent for the latitude of interest at a constant depth. The ocean model shows 4.8 ± 0.4 °C at 1,000 m and 9.4 ± 1.0 °C at 500 m throughout the western Pacific vent fields. On average, larvae of vent barnacles, genus Neoverruca, widely encountered in western Pacific vent fields, require 99 d at 4 °C (∼1,000 m) and 50 d at 10 °C (∼500 m) to reach the last larval life stage (34). These data suggest that PLD is a function of the depth at which larval dispersal occurs; that is, the deeper the dispersal depth, the longer the PLD.

To express this temperature dependence of larval development, for the sake of simplicity, we used a unified model deduced from published experimental laboratory studies, mostly for shallow-water vertebrates and invertebrates (35). Population-averaged PLD (mean of species-specific values) is given as 83 d at 1,000 m and 43 d at 500 m (Methods). This represents the vent barnacle case described earlier reasonably well.

Potential Larval Dispersal in the Okinawa Trough.

The Lagrangian PDF corresponding to a PLD of 83 d suggests that all vent fields (deeper than 1,000 m) should be within reach of Hatoma Knoll (Fig. 2B) if dispersal trajectories maintain that initial depth. Potential larval transport from Hatoma Knoll to other vent fields can be deduced from the Lagrangian PDF by multiplying the PDF at a destination site by its representative area. Assuming a vent area radius of 1 km, for instance, transport from Hatoma Knoll to the neighboring Irabu Knoll (∼100 km) at depth of 1,000 m is realized 8,571 times in 100 million independent dispersal events. As another example, transport from Hatoma to the furthest point in the Okinawa Trough, Iheya Ridge (∼400 km), is 567 in 100 million independent events. Assuming that the dispersal pattern or direction from Hatoma Knoll changes every 2 wk, there are 26 statistically independent dispersal events (float releases) per year or 100 million dispersal events in 3.8 million years. Hence, the numbers in Fig. 2B can be regarded as the expected number of times larvae would be transported in 3.8 million years, close to a typical lifetime of a spreading center in the back-arc basins of the Western Pacific (5–10 million years).

In terms of frequency, connections from Hatoma Knoll to neighboring Irabu Knoll could occur once every ∼400 y. Similarly, we can estimate potential larval dispersal from each of the vent fields in the Okinawa Trough (Fig. 3B). By accounting for all possibilities, larval transport between Hatoma Knoll and all other vent fields could occur every ∼80 y at 1,000 m depth. As more vent fields are continually being discovered, actual larval transport may be more frequent than estimated here. In September 2014, for example, a large tract of vent chimneys (1,500 m × 300 m) was discovered between known vent fields in the Central and Southern Okinawa Trough.

Vent fields within back-arc basins could be well connected, whereas basin-to-basin transport shows dispersal barriers and directionality. (A) Potential larval dispersal from western Pacific vent fields quantified from the biophysical model (lines and numbers). Dispersal depth is assumed to be 1,000 m. PLD is set to 83 d. White ovals show 11 geographically separated regions defined in this study. Line colors show the direction of connections (see the circular diagram in the figure). For an explanation of the numbers, refer to the Fig. 2 legend. Close-up views of the (B) Okinawa Trough, (C) Manus Basin, and (D) Lau Basin suggest that back-arc basins should form well-mixed pools without directionality. (E) The gap between North Fiji and Woodlark could be bridged with above-average PLD (∼twice the mean). When there were multiple vent fields within a 30-km radius, only one of them was randomly selected so as to avoid graphical complications. See Movie S1 for dispersal patterns from all selected vent fields.

These timescale estimates depend on accurate assessment of independent dispersal events. Potential larval dispersal will be more frequent if the Eulerian correlation time is shorter than our estimates. Consideration of additional biological traits (e.g., seasonal spawning) will reduce the estimated independent dispersal events and resulting connectivity.

Potential Larval Dispersal from the Western Pacific Vents.

Using this modeling framework, we assessed potential larval dispersal among all vent fields in the entire western Pacific Ocean. To assess basin-to-basin transport, we grouped vent fields into 12 geographically separated regions (Fig. 3). Although four of these regions (Izu-Bonin, Solomon, New Hebrides, and Kermadec) are relatively young and have not fully developed back-arc basins, we included them because of their potential as stepping stones to connect distant basins.

To the best of our knowledge, quantitative information for ontogenetic vertical migration of vent animals is very scarce (36) and is not available relative to larval developmental stages. We tested cases with dispersal depths of 100–1,500 m below the sea surface. Only active, confirmed vent fields deeper than a given dispersal depth were included in the analysis. As a default case, we show potential larval transport at a dispersal depth of 1,000 m for a mean PLD of 83 d.

For the 1,000-m dispersal case, there are four potential basin-to-basin connections with distinctive directionality and four regions (Okinawa, Izu-Bonin, Solomon, and Kermadec) that are isolated (Fig. 3A). Unidirectional transport is predicted from South Mariana to North Mariana, from Woodlark to Manus, and from Lau-Tonga to the North Fiji region. Only the North Fiji and New Hebrides regions could be connected in both directions. Long dispersal connecting these distant basins could occur 32–747 times in 100 million independent dispersal events. In other words, these connections could be successful once every ∼5,000 to ∼12,000 y, assuming a 2-wk Eulerian correlation time. Westward transport in the Southern Hemisphere should reflect the deep South Equatorial Current system (27).

Close-up views of potential larval dispersal in the Okinawa Trough, Manus Basin, and Lau Basin (Fig. 3 B–D) show that vent fields could be well connected within back-arc basins without particular directionality. Within each of these back-arc basins, one vent field could be connected with many others, and larval dispersal would be mostly bidirectional, unlike long-distance basin-to-basin transport.

Other Combinations of Dispersal Depths and PLD.

Transport patterns were similar at dispersal depths of 100–1,500 m for mean PLDs, except for the northwest Pacific, where the strong Kuroshio Current enables long-distance connections for shallower dispersal depths (within the upper ∼600 m). Vent fields in the Okinawa Trough and the Izu-Bonin Arc (∼1,200 km apart) can be bridged by the Kuroshio Current (Fig. S1). Also, communication is established between Izu-Bonin and Northern Mariana, which is associated with meandering of the Kuroshio Current (Fig. S1).

Larval transport among vent fields may be similar regardless of dispersal depth, except for regions affected by the Kuroshio Current. (A) Potential larval dispersal of the western Pacific vent fields for a dispersal depth of 500 m (lines and numbers), where PLD is set to the population mean of 43 d. See the legends of Figs. 2 and 3 for details. Close-up views showing unidirectional transport (B) from Okinawa to Izu-Bonin and (C) from Lau to North Fiji, following the Kuroshio Current and the South Equatorial Current, respectively. The overall pattern does not change much from the 1,000-m case (Fig. 3), with the exception of regions affected by the Kuroshio Current. (D) The southwest Pacific vent complex could be completely interconnected with above-average PLD (∼twice the mean), based on mostly westward transport.

There are two counteracting effects as a function of dispersal depth. As dispersal depth becomes shallower, current speed increases, which should extend larval dispersal distance, but at the same time, PLD diminishes, which limits dispersal distance. Our model suggests these two counteracting effects should nearly cancel each other, resulting in similar transport patterns regardless of dispersal depth, except for regions affected by the Kuroshio Current. Ontogenetic vertical migration of vent larvae may substantially alter dispersal distance in the northwest Pacific, but less in other regions.

The cases presented here assume population mean PLDs. Larval dispersal from one basin to neighboring regions may be achieved even with below-average PLDs. For a dispersal depth of 500 m, transport from the Okinawa to the Izu-Bonin region could be established for a PLD of 20 d or longer. Species with above-average PLDs will disperse longer distances and may reach more distant vent fields. Gaps between the New Hebrides and Woodlark regions could be bridged by the South Equatorial Current. All vent fields in the southwest Pacific complex may be connected for long dispersers with PLDs of two or more times the mean (Fig. 3E). This extended connection would be relatively infrequent, occurring once every hundreds of thousands of years.

Nonetheless, there remain clear gaps even with longer PLDs. The Okinawa Trough is almost completely sealed if dispersal depth is deeper than 600 m. Gaps between vents in the southwest and northwest Hemispheres may be too large to be spanned by realistic PLDs. It has been reported that larvae of cold-seep mussels, Bathymodiolus childressi, may disperse at depths as shallow as 100 m for more than a year (37). This is rather an extreme combination of PLD and dispersal depth compared with population mean PLDs of shallower species (12 d). Our model suggests that even with a PLD of 1 y at 100 m, the Mariana Trough and Manus Basin should not be directly connected, because the Equatorial Countercurrent inhibits transport across the Equator at a dispersal depth of 100 m. Ocean circulation processes imply that there should be other means that enable the connection across the Equator (e.g., undiscovered vents, whale carcasses, and cold seeps as stepping stones).

Comparisons with Population Genetic Data.

A recent population genetic study, using mitochondrial DNA and microsatellite markers, revealed that populations of the vent-restricted gastropod, Ifremeria nautilei, in the Manus Basin were genetically distinct from those of the North Fiji and Lau Basins (14). Estimates of gene flow also implied migration from the Lau to North Fiji Basin with a splitting time of tens of thousands of generations and genetic isolation between those two Basins and the Manus Basin for several hundred thousand generations. Our biophysical model, in contrast, predicts that unidirectional larval transport from the Lau to North Fiji vent fields should occur only once in tens of thousands of years. Our model also suggests that using the New Hebrides and Solomon arcs as stepping stones, the connection can be further extended all of the way to the west end of the Manus Basin once in hundreds of thousands of years for species with longer PLDs (Fig. 3E). These genetic estimates agree with our flow-based assessment, assuming that the generation time of Ifremeria is on the order of a year. Thus, the rather weak gene flow from Lau to North Fiji and the genetic barrier between Manus and North Fiji can be explained by the ocean circulation.

Population genetics of Neoverruca barnacles, based on the mitochondrial cytochrome c oxidase subunit I gene, show no significant genetic differentiation among populations within the Okinawa Trough (12). Furthermore, haplotype analyses of the barnacles imply that Neoverruca populations inhabiting the Izu-Bonin region originated in the Okinawa Trough, although these two populations are genetically distinct (12). Our model predicts that within the Okinawa Trough, a vent field can be interconnected with other vent fields on average once every ∼80 y at a dispersal depth of 1,000 m. Given that more vent fields are being discovered, actual larval exchange should be even more frequent, which may result in well-mixed genetic pools. Transport from the Okinawa Trough to the Izu-Bonin Arc is predicted to be less frequent, once every tens of thousands of years, which apparently is not frequent enough to prevent genetic differentiation.

Dispersal Patterns in the Past.

The dispersal assessment of this study was based on present-day oceanographic information. Estimates are not necessarily applicable to the past, when currently active basins started spreading. The present global, thermohaline oceanic circulation commenced ∼38 million years ago, when substantial Antarctic sea ice began to form (38). The earth has experienced glacial and interglacial periods since then. During glacial periods, warm, thermohaline return flow may have weakened, and monsoon circulation could have been intensified in winter, but overall ocean circulation patterns were likely similar to the present pattern (39). We believe that quantified dispersal patterns and scaling analyses of this study are reasonable and applicable to the past 5–10 million years. However, there may have been prehistoric larval transport among some presently disconnected vent fields. Paleo-oceanographic information will be important to accurately estimate gene flow among contemporary vent species.

Further study based on network analysis would be useful in identifying key sites for effective conservation. Optimal designs for marine protected areas will require consideration of appropriate spatial and temporal scales. To assess resilience of vent communities and to facilitate their recoveries from natural and anthropological disturbances, it will be necessary to understand connectivity on intraregional scales in greater detail (40). Information from this study will also be valuable in environmental assessment; for example, to identify potential deep-ocean mining sites with minimal (or maximal) risk to vent communities. Near-bottom circulation processes in back-arc basins may be less important than those of midocean ridges, because of the lack of conduit-like topographic features. However, accurate predictions of bottom boundary layers will be of importance for assessment of self-recruitment.

Quantitative data describing deep-ocean dispersal processes are limited. One might think that existing Argo float data (41) could fill this void. However, a majority of Argo floats used Argos satellite communications, which necessitate long drift times on the sea surface during data uploads. Cycle times of Argo floats (essentially the time spent in deep water) are mostly 10 d or less, which is much shorter than the 30-d cycle time used in our experiments. Time-series based on Argo float surfacing points do not accurately represent deep ocean circulation because they are heavily influenced by strong surface currents. Among existing Argo floats in the Pacific Ocean, we found only two units that could be used to examine dispersal patterns emanating from western Pacific vent fields (one from the 13 N Ridge Site and the other from the Alice Springs Field). More observation data are required to fully examine the dispersal estimates from this study.

Drift at the Sea Surface

Floats spend ∼15 min on the sea surface for satellite communications and ∼125 min ascending and descending. This is substantially less than the drift time at 1,000 m (30 d). However, the speed of the surface current is much faster than that at 1,000 m; hence, drift distance near the surface could potentially be substantial, thereby invalidating this analysis. We assessed this near-surface drift by introducing an extra float that surfaced much more frequently, every 6 h, instead of every 30 d. The drift distance of this extra float (distance between consecutive surfacing locations) was found to be 2.4 ± 1.3 km, whereas that of the regular 30-d-cycle float was 40 km on average. Comparison of these two cases suggests that ∼92% of the drift distance for the 6-h-cycle float was a result of the near-surface drift (at the surface and during descending/ascending, combined). The drift distance of the 30-d-cycle floats, therefore, are mostly (∼94%) as a result of deep ocean circulation, and their drift histories give us a sense of dispersal at 1,000 m in depth.

Methods

The model domains covered all active western Pacific vent fields between 32°N and 36°S registered in the InterRidge vents database (29). The latest version of the 3D hydrodynamic model Regional Ocean Modeling System is used to integrate the rotating primitive equations with a realistic equation of state (42, 43). There are two domains with a 5-km mesh resolution: one covering the northwest Pacific Ocean (43°N–15°S) and the other including the southwest Pacific Ocean (40°S–10°N) with substantial overlap around the equatorial Manus Basin. Two semiclosed basins, the Okinawa Trough and the Manus Basin, are discretized with a finer 1-km mesh, including eight tidal constituents. The model domains and time-lapse movies of ocean circulation processes are provided in Detailed Model Configuration and Movie S2 and S3. More than 1 million (1,098,000) simulated model floats were released from each of the vent fields in the model and randomly distributed (uniform distribution) within 5-km radii of registered vent locations: 250 floats every 3 h from April 1 through September 30 of 2011–2014.

10 OPTIMARE NEMO-Floats, developed on the basis of the SOLO-Float for the Argo program (41, 44), were deployed above Hatoma Knoll (123.8410°N, 24.8550°E). Parking depth was set to 1,000 m. The mean descending (ascending) speed of the floats was set to a relatively fast 50 cm/s (18 cm/s) to minimize drift occurring during descent/ascent. Floats spend ∼15 min on the sea surface for satellite communications and ∼125 min ascending and descending. Cycle times of floats are set to 30 d. Our estimates indicate that cycle times should be 30 d or longer so that surface drifting distances <5% of total travel distance (Drift at the Sea Surface).

We use a unified model proposed by O’Connor et al. (35) to account for the temperature dependence of larval development in marine animals. Deduced from 69 species, PLD is represented as a function of water temperature by ln (PLD) = B0 − 1.34 × ln (T/Tc) − 0.28 × [ln (T/Tc)]2, where T is ocean temperature and B0 is the value of ln (PLD) at Tc = 15 °C. To describe a generic case of larval dispersal processes, we use B0 = 3.17, which describes the population mean PLD as a default case (35), and B0 = 10.0 for a longer PLD case (twice the mean). We assumed that metabolic rates of vent animals are relatively insensitive to hydrostatic pressure (45).

Detailed Model Configuration

The bottom topography is sampled from the 30 arc-second global bathymetry grid (SRTM30_PLUS) based on the satellite-gravity model (46). Model domains are discretized with 40 terrain-following vertical layers. The flow is forced at the sea surface by daily momentum, heat, and freshwater fluxes from the 55-y data reanalysis by the Japan Meteorological Agency (47). Initial and lateral boundary conditions are set by the 0.25° data assimilation product (PSY3V3R3) of the Mercator Ocean (48). Major tidal constituents (m2, s2, n2, k2, k1, o1, p1, and q1) of the global inverse tide model (TPXO7.2 Atlas) are included at the lateral boundaries of the inner 1-km domains (49, 50). Particle velocities were obtained by linearly interpolating velocity fields of the ocean circulation model at particle positions and including subgrid-scale diffusion (33). Particle trajectories were obtained by integrating particle velocities over a given advection time with 900-s time stepping. The Lagrangian PDF was assessed by filtering (Gaussian filter) frequencies of the model float distribution (i.e., counts of model floats in each grid cell of the model) with varying filter size (SD) proportional to the spatial extent of the model particle distribution (one-tenth of the diagonal length or smaller, depending on topographic constraints). For more detailed description of the PDF method and the equivalent particle equation, see ref. 33.

Acknowledgments

Comments from and discussions with Dennis McGillicuddy, Lauren Mullineaux, Tadashi Maruyama, Yasuo Furushima, Yoshihiro Fujiwara, Masako Nakamura, and Mary Grossmann were helpful in focusing this contribution. We thank Shohei Nakada and the 11th Regional Coast Guard Headquarters, Naha, Okinawa, for aiding in many aspects of this work. We thank Steve Aird for his careful editing. This work was supported by a Canon Foundation Grant (2011–2014) and internal funding from the Okinawa Institute of Science and Technology Graduate University.

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